City stockbrokers are considering lodging an official complaint after the Government’s decision to reject the majority of applications for Royal Mail shares cost them millions in lost commissions.

The brokers argue that the decision to reject orders rather than scale them back was unfair on them as well as on investors. They plan to lodge their complaint with Vince Cable, the Business Secretary, or the business minister, Michael Fallon.

Both ministers will today review the launch of Royal Mail’s historic share offer, the allocation of shares and the conditional trading so far. After being priced at 330p a share, the stock rose 38pc on the first day of trading. Applications for shares by 500 institutional investors were rejected, along with any individual requests for shares worth more than £10,000.

Traders said the Government’s insistence that only 10pc of the institutional offering went to hedge funds led to a lack of liquidity because institutional investors were not selling.

However, Greg Bennett, head of capital markets at Fidelity Worldwide Investment, said: “The allocation of institutional shares was focused on long-term investors who are best aligned to the future success of the Royal Mail. This is the only opportunity the company will have to influence who the shareholders are, so the emphasis on long-term investors is the right approach.”

A government official said ministers would review glitches, such as the collapse of Hargreaves Lansdown’s website on Friday. Many small investors rushed to sell 227 Royal Mail shares they were allocated on Thursday night after the stock opened up 36pc on Friday morning. However, hundreds of small investors at Hargreaves Lansdown were prevented from trading after intense demand caused a glitch in its systems. Royal Mail will be openly traded on the London Stock Exchange from tomorrow.